Propagation of a topologically half-charge vortex light beam in a self-focusing photorefractive medium

While a fundamental Gaussian light beam can form stably a spatial soliton in certain self-focusing medium, a single-wave topologically integer-n-charge vortex light beam cannot. It breaks up into 2n filaments due to symmetry breaking and azimuthal instability, in which every azimuthal section of a π phase range from a soliton and repels itself from its azimuthal neighboring soliton. Then what happens to the half-charge vortex light beam, which contains only one section of a π phase range? We investigate experimentally and theoretically the propagation and stability of a topologically half-charge vortex light beam in a self-focusing photorefractive medium. We observed that the light beam propagates unstably in a self-focusing medium and breaks up into three filaments. This result is confirmed by numerical simulation and perturbation analysis.